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Proof step 6 from proof validref-class-rec-better-keep (previous step)

is_obj(str, r, st), validref(str, r, ty, st) ⊦ st[r -- _type] .type ≤ ty ∧ ( ¬ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∨ st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref ∨ st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validref-class-rec-better antecedent: succedent: is_obj(str, r, st) → ( validref(str, r, ty, st) ↔ st[r -- _type] .type ≤ ty ∧ ¬ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ ¬ validref (str, st[r -- fs '] .refval, fs .type, st)))) substlist: [st, ty, r, str] → [st, ty, r, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r, str)]]